This chapter discusses quantum phase transitions (QPT). It starts with a brief review of thermal phase transitions, critical exponents and scaling laws. The scaling laws are then generalized to the QPT case which is also illustrated with two specific examples. The first example that of the one-dimensional Ising model in a transverse magnetic field; the second is that of the bosonic Hubbard model. Quantum Monte Carlo is described briefly and mean field theory is introduced with the help of several examples and exercises.
Keywords: quantum phase transition; critical exponents; scaling laws; quantum Monte Carlo; mean field theory
Chapter. 18519 words. Illustrated.
Subjects: Mathematical and Statistical Physics
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